What is the answer to x=ln(-2x) ?

The answer to x=ln(-2x) is x=-\W_{0}(1/2)

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x=ln(-2x)

x = ln (- 2 x)

x = - W_{0} (\frac{1}{2})

Solution steps

x = ln (- 2 x)

f (x) = g (x),

then

a^{f (x)} = a^{g (x)}

e^{x} = e^{l n (- 2 x)}

Simplify

e^{l n (- 2 x)} : - 2 x

e^{x} = - 2 x

Solve

e^{x} = - 2 x : x = - W_{0} (\frac{1}{2})

x = - W_{0} (\frac{1}{2})

Verify Solutions:

x = - W_{0} (\frac{1}{2})

True

The solution is

x = - W_{0} (\frac{1}{2})

5 ln (5 x + 1) + 3 = - 7

ln (x + 2) - ln (x - 2) = 1

(x + 1) = lo g_{10} (x - 1) + 3

lo g_{4} (x + 20) = 3

ln (x) - ln (x + 1) = 5